4.5 Stationary and progressive waves

Question 1

What sort of sound is made if a guitar string is plucked gently at its centre

Answer 1

Constant frequency as a stationary wave of constant frequency is set up on the string.

Question 2

What sort of sound is made if a guitar string is plucked harshly

Answer 2

The string vibrates in a more complicated way and the note produced contains other frequencies as well as the frequency produced when it is plucked gently

Question 3

When is a stationary wave formed

Answer 3

When two progressive waves pass through each other

Question 4

How can you form a stationary wave with string

Answer 4

Fix both ends and make the middle part vibrate so progressive waves travel towards each end, reflect at the ends, and then pass through each other.

Question 5

What is the first harmonic referred to as

Answer 5

The fundamental

Question 6

Describe the fundamental

Answer 6

Consists of a single loop that has a node at either end. Has an antinode (where it vibrates with maximum amplitude midway.

Question 7

Distance between adjacent nodes

Answer 7

1/2λ

Question 8

Stationary waves that vibrate freely do not…

Answer 8

…transfer energy to their surroundings

Question 9

Why don’t stationary waves transfer energy to their surroundings

Answer 9

The amplitude of vibration is zero at the nodes so there is no energy at the nodes. The amplitude of vibration is a maximum at the antinodes, so there is maximum energy at the antinodes. As the nodes and antinodes are at fixed positions, no energy is transferred in a freely vibrating stationary wave pattern.

Question 10

In general, in any stationary wave pattern:

Answer 10

The amplitude of a vibrating particle in a sationary wave pattern varies with position from zero at a node to maximum amplitude at an antinode.
The phase difference between two vibrating particles is zero if the two are between adjacent nodes or separated by an even number of nodes, 180° (=πradians) if the two particles are separated by an odd number of nodes

Question 11

Frequency in a stationary wave

Answer 11

All particles except those at the nodes vibrate at the same frequency

Question 12

Frequency in a progressive wave

Answer 12

All particles vibrate at the same frequency

Question 13

Amplitude in a stationary wave

Answer 13

Varies from zero at the nodes to a maximum at the antinodes

Question 14

Amplitude in a progressive wave

Answer 14

The amplitude is the same for all particles

Question 15

Phase difference between two particles in a stationary wave

Answer 15

Equal to mπ, where m is the number of nodes between the two particles

Question 16

Phase difference between two particles in a progressive wave

Answer 16

Equal to 2πd/λ where d=distance apart and λ is the wavelength

Question 17

Sound in a pipe - stationary wave example

Answer 17

Sound resonates at certain frequencies in an air-filled tube. If a pipe is closed at one end, these resonant frequencies occur when there is an antinode at the open end and a node at the other end

Question 18

Microwaves - stationary wave example

Answer 18

Microwaves from a transmitter are directed normally at a metal plate, which reflects the microwaves back towards the transmitter. When a detector is moved along the line between the transmitter and the metal plate, the detector signal is found to be zero at equally spaced positions along the line. The reflected waves and the waves from the transmitter form a stationary wave pattern. The positions where no signal (or a minimum) is detected are where nodes occur. They are spaced at intervals of half a wavelength